It is well known to obtain three-dimensional arrays of data representing one or more physical properties at regular grid positions within the interior of solid bodies. Such data can be obtained by non-intrusive methods such as computed axial tomographic (CAT) x-ray scanning systems, by nuclear magnetic resonance (NMR) imaging systems, or by other non-intrusive mechanisms such as ultrasound, positron emission tomography (PET), emission computed tomography (ECT) and multimodality imaging (MMI). Each of these techniques produces a planar, grid-like array of values for each of a succession of slices of the solid object, thus providing a three-dimensional array of such values. Typically, the solid object is a human body or a portion thereof, although the method is equally applicable to other natural or artificial bodies. In the case of CAT scanning, the physical value would be the coefficient of x-ray absorption. For NMR imaging, the physical value would be the spin-spin or the spin-lattice relaxation time. In any event, the measured physical values reflect the variations in composition, density or surface characteristics of the underlying physical structures. Such a three-dimensional data array typically consists of a plurality of sets of three-dimensional (x, y, z) coordinates distributed at regular positions in a cubic or parallelepiped lattice within the body, and at least one value (V.sub.xyz) of the physical property being associated with each respective one of the coordinate positions. Each cubically adjacent set of eight such positions defines a cubic volume called a "voxel" with a physical property value being specified for each of the eight voxel vertices. In turn, each voxel "neighborhood" includes the voxel itself and the immediately adjacent six voxels which share a common face; thus, a voxel neighborhood is a cubic volume including seven voxels having 32 physical values associated with the voxel vertices.
It is likewise known to utilize such three-dimensional arrays of interior physical values to generate visual images of the interior structures within the body. In the case of the human body, the visual images thus produced can be used for medical purposes such as diagnostics or for the planning of surgical procedures. In order to display two-dimensional images of such three-dimensional interior structures, however, it is necessary to locate the position of the surface of such structure within the array of physical values. This is accomplished by comparing the array values to a single threshold value, or to a range of threshold values, corresponding to the physical property values associated with that surface. Bones or any other tissue, for example, can be characterized by a known range of density values to which the array values can be compared. Once the surface location is determined, this surface must be shaded so as to give the human eye the correct impression of the shape and disposition of that surface when it is displayed on a two-dimensional display device. To provide such shading, the angular direction of a vector normal to the surface at each point on the surface is compared to the viewing angle of the observer. The intensity of shading can then be adjusted so as to be proportional to the difference between these angles. Such angular difference information can also be used to control the colors incorporated in the displayed images, thus providing yet another visual clue to the surface disposition. Normal vectors with components directed away from the viewing angle can be ignored since the associated surfaces are hidden from view.
One method for approximating the surface of an internal structure is the so-called "marching cubes" method, disclosed in H. E. Cline et al. U.S. Pat. No. 4,710,876, granted Dec. 1, 1987, and assigned to applicants' assignee. In this method, the surface segment intersecting a voxel is approximated by one of a limited number of standardized plane polygonal surfaces intersecting the voxel. One particular standardized surface is selected by a vector representing the binary differences between the threshold value and the eight voxel vertex values. The surface-to-voxel intersection coordinates, as well as the normal vector, for each such standardized polygonal surface set can then be calculated or obtained by table look-up techniques. The final surface is assembled as a mosaic, using all of the standardized polygons as tessera or tiles. Appropriate intensity values derived from the normal vector angles can be displayed immediately for viewing, or stored for later display. H. E. Cline et al. U.S. Pat. No. 4,729,098, granted Mar. 1, 1988, and also assigned to applicants' assignee, shows a variation of the marching cubes method using nonlinear interpolation to locate more accurately the coordinates of the tessellated standardized polygons.
Another method for approximating the surface of an internal structure is the so-called "dividing cubes" method, disclosed in H. E. Cline et al. U.S. Pat. No. 4,719,585, granted Jan. 12, 1988, and also assigned to applicants' assignee. In this method, the values at the vertices of the voxel are used to interpolate, in three dimensions, values at regularly positioned intra-voxel sub-grid locations. These interpolated sub-grid values can then be used to locate the surface position more precisely and to calculate the normal vector more accurately. The marching cubes and dividing cubes algorithms are further described in "Two Algorithms for the Three-Dimensional Reconstruction of Tomograms," by H. E. Cline et al., Medical Physics, Vol. 15, No. 3, p. 320, May/June 1988.
In order to distinguish between different internal structures with the same or similar physical property values , W. E. Lorensen et al. U.S. Pat. No. 4,751,643, granted Jun. 14, 1988, and likewise assigned to applicants' assignee, discloses a technique for labeling surfaces with similar property values and using adjacency criteria with respect to a "seed" location in the particular structure of interest to segregate the desired surface from all of the labeled surfaces. The copending application of H. E. Cline et al., Ser. No. 907,333, filed Sep. 15, 1986, now U.S. Pat. No. 4,791,567, also assigned to applicants' assignee, discloses another technique of segregating similar structures by determining connectivity from adjacency information. More particularly, adjacency is determined independently for each slice in the data store array, and thereafter adjacency is determined between slices. Copending application Ser. No. 943,357, filed Dec. 19, 1986, now U.S. Pat. No. 4,879,668, for H. E. Cline et al., and also assigned to applicants' assignee, discloses yet another technique for differentiating internal structures in which a linear pass is made through the data array to locate and label all of the different structures along the scan line by counting structure interfaces. It is apparent that there are formidable obstacles to establishing the connectivity of surface data points in a three-dimensional array of data while discriminating against similar but unconnected surfaces.
While use of a single array of values of a physical property within the interior of a solid body to generate perspective images of arbitrarily selected internal structures within the body, seen as if viewed from arbitrarily chosen viewing angles, all by manipulating the selfsame single array of values, is known, some structures in the interior of the human body unfortunately have not responded well to this imaging technique. Closely adjacent and intermingled tissues with the same or closely similar values of the scanned physical property, for example, have been difficult or impossible to discriminate between. Attempts to image such tissues result in an image including multiple tissues with inadequate or concealed details. Blood vessels are one type of tissue which is particularly difficult to discriminate for these reasons. A similar kind of problem, and one solution to the problem, is discussed in "3D Reconstruction of the Brain from Magnetic Resonance Images Using a Connectivity Algorithm," by H. E. Cline et al., Magnetic Resonance Imaging, Vol. 5, No. 5, p. 345, 1987.
Nuclear magnetic resonance (NMR) imaging is better at contrasting soft tissues than CAT x-ray scans, but suffers from the fact that there are many more soft tissue surfaces that are identified by any given threshold surface value, as compared to surfaces such as bone and organs. The difficulty with the connectivity algorithms of the prior art in situations where surface values are close to each other is that they examine all adjacent voxels in order to find voxels intersecting the surface of interest. This procedure inherently tends to bridge to tissues with similar surface values even though the surfaces are not in fact connected. An additional problem with the prior art technique is the greatly increased amount of processing necessary to examine all of the adjacent voxels, increasing the delay in generating an image while at the same time producing images with inferior surface discrimination. The problem becomes particularly acute for three-dimensional vascular imaging, where the large number of closely spaced blood vessels accentuate the surface discrimination problem.
The connectivity algorithm described in the above-mentioned Magnetic Resonance Imaging article can be called a volume-dependent algorithm in that all of the voxels immediately adjacent to the faces of a seed voxel (i.e., all of the volume surrounding the seed voxel) are examined for surface intersections. Since other surfaces with the same or similar surface constants could also intersect such adjacent voxels, there exists the possibility of bridging to adjacent but actually unconnected surfaces. The problem of preventing bridging by better discriminating between closely intermingled surfaces with similar surface constants in three-dimensional imaging systems is of considerable concern in soft tissue imaging.
Accordingly, one object of the invention is to provide a method and apparatus for displaying images of interior surfaces within solid bodies, with good discrimination between surfaces that are closely intermingled.
Another object is to provide a three-dimensional imaging system and method wherein images of closely intermingled surfaces with similar surface physical property values are clearly discriminated without an undue amount of processing.
Another object is to provide a scanning method and apparatus for displaying images of interior portions of a human body with good discrimination between closely adjacent tissues having the same or closely similar values of the scanned physical property.